Finite Group Databasebeta

← C3×D3×#13133721 #44501814

Subgroups — C3×D3×#13133721 #44501814

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#13133721C211yesmaximal, characteristic, complemented, Hall
2D3×#13133721C311yesmaximal, characteristic, direct product factor
3C2×C3×#13133721—31nomaximal
4C3×D3×C11×C31C511yesmaximal, characteristic, complemented, Hall
5C3×#13133721—21no—
6C3×#13133721D311yescharacteristic, direct product factor
7C3×#13133721C2×C311yescharacteristic, complemented
8C2×#13133721—31noHall
9C32×C11×C31C2×C511yescharacteristic, complemented, Hall
10C3×D3×ΓL(1,𝔽32)—111nomaximal, Hall
11D3×C11×C31C3×C511yescharacteristic, complemented
12C2×C3×C11×C31—31no—
13#13133721C3×D311yescharacteristic, direct product factor, Hall
14C32×ΓL(1,𝔽32)—111noHall
15C3×C11×C31—21no—
16C3×C11×C31C5×D311yescharacteristic, complemented
17C3×C11×C31C2×C3×C511yescharacteristic, complemented
18C3×D3×C11⋊C5—311nomaximal, Hall
19C2×C3×ΓL(1,𝔽32)—331no—
20D3×ΓL(1,𝔽32)—111no—
21C2×C11×C31—31noHall
22C3×D3×C31C11⋊C511yescharacteristic, complemented, Hall
23C32×C11⋊C5—311noHall
24C3×ΓL(1,𝔽32)—111no—
25C3×ΓL(1,𝔽32)—111no—
26C3×ΓL(1,𝔽32)—221no—
27C11×C31C3×C5×D311yescharacteristic, complemented, Hall
28C2×C3×C11⋊C5—931no—
29D3×C11⋊C5—311no—
30C2×ΓL(1,𝔽32)—331noHall
31C32×C31C2×C11⋊C511yescharacteristic, complemented, Hall
32C3×D3×C11ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
33C2×C3×C31—31no—
34D3×C31C3×C11⋊C511yescharacteristic, complemented
35C3×C11⋊C5—311no—
36C3×C11⋊C5—311no—
37C3×C11⋊C5—621no—
38ΓL(1,𝔽32)—111noHall
39C2×C11⋊C5—931noHall
40C32×C11C2×ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
41C3×C31—21no—
42C3×C31D3×C11⋊C511yescharacteristic, complemented
43C3×C31C2×C3×C11⋊C511yescharacteristic, complemented
44C3×C5×D3—3411noHall
45C2×C3×C11—31no—
46D3×C11C3×ΓL(1,𝔽32)11yescharacteristic, complemented
47C2×C31—31noHall
48C11⋊C5—311noHall
49C32×C5—3411noHall
50C3×C11—21no—
51C3×C11D3×ΓL(1,𝔽32)11yescharacteristic, complemented
52C3×C11C2×C3×ΓL(1,𝔽32)11yescharacteristic, complemented
53C31C3×D3×C11⋊C511yescharacteristic, complemented, Sylow
54C2×C3×C5—10231no—
55C5×D3—3411no—
56C2×C11—31noHall
57C3×D3#1313372111yescharacteristic, direct product factor, Hall
58C3×C5—3411no—
59C3×C5—3411no—
60C3×C5—6821no—
61C11C3×D3×ΓL(1,𝔽32)11yescharacteristic, complemented, Sylow
62C2×C5—10231noHall
63C32C2×#1313372111yescharacteristic, complemented, Sylow
64C2×C3—31no—
65D3C3×#1313372111yescharacteristic, direct product factor
66C5—3411noSylow
67C3—21no—
68C3C2×C3×#1313372111yescharacteristic, complemented
69C3D3×#1313372111yescharacteristic, direct product factor
70C2—31noSylow
subgroupG/H
center, hypercenterC3D3×#13133721
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×#13133721C2semidirect
2. D3×#13133721C3direct (N × H)
4. C3×D3×C11×C31C5semidirect
6. C3×#13133721D3direct (N × H)
7. C3×#13133721C2×C3semidirect
9. C32×C11×C31C2×C5semidirect
11. D3×C11×C31C3×C5semidirect
13. #13133721C3×D3direct (N × H)
16. C3×C11×C31C5×D3semidirect
17. C3×C11×C31C2×C3×C5semidirect
22. C3×D3×C31C11⋊C5semidirect
27. C11×C31C3×C5×D3semidirect
31. C32×C31C2×C11⋊C5semidirect
32. C3×D3×C11ΓL(1,𝔽32)semidirect
34. D3×C31C3×C11⋊C5semidirect
40. C32×C11C2×ΓL(1,𝔽32)semidirect
42. C3×C31D3×C11⋊C5semidirect
43. C3×C31C2×C3×C11⋊C5semidirect
46. D3×C11C3×ΓL(1,𝔽32)semidirect
51. C3×C11D3×ΓL(1,𝔽32)semidirect
52. C3×C11C2×C3×ΓL(1,𝔽32)semidirect
53. C31C3×D3×C11⋊C5semidirect
57. C3×D3#13133721direct (N × H)
61. C11C3×D3×ΓL(1,𝔽32)semidirect
63. C32C2×#13133721semidirect
65. D3C3×#13133721direct (N × H)
68. C3C2×C3×#13133721semidirect
69. C3D3×#13133721direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#131337212
D3×#131337213
C2×C3×#131337213
C3×D3×C11×C315
C3×D3×ΓL(1,𝔽32)11
C3×D3×C11⋊C531